Finite Group Databasebeta

← C2×#20253989 #27086050

Subgroups — C2×#20253989 #27086050

Order 12032.

1986 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689675C211yesmaximal, characteristic, complemented
2C2×#15689659C211yesmaximal, characteristic
3#20253989C2116yesmaximal, direct product factor
4C2×#15689530C211yesmaximal, characteristic, complemented
5C2×#15689516C211yesmaximal, characteristic, complemented
6C2×#15689490C211yesmaximal, characteristic, complemented
7C2×#15689484C211yesmaximal, characteristic, complemented
8C2×#15689379C211yesmaximal, characteristic, complemented
9C2×#15689371C211yesmaximal, characteristic
10C2×#15689369C211yesmaximal, characteristic
11C2×Q16×Dic47C211yesmaximal, characteristic, complemented
12C2×#15689215C211yesmaximal, characteristic, complemented
13C2×#15689210C211yesmaximal, characteristic, complemented
14C2×#15689208C211yesmaximal, characteristic, complemented
15C2×M16×Dic47C211yesmaximal, characteristic, complemented
16C2×C47×#470C211yesmaximal, characteristic, complemented
17C22×#10625337C2211yescharacteristic
18C22×#10625325C2211yescharacteristic
19C22×#10625336C2211yescharacteristic
20C22×#10625329C2211yescharacteristic
21#15689675—24no—
22#15689675C2218yescomplemented
23C2×#13094023C2211yescharacteristic
24C2×#13094022C2211yescharacteristic
25#15689659—24no—
26#15689659C2218yes—
27C2×#13094019—21no—
28C2×#13094015C2211yescharacteristic
29C2×#13094014—21no—
30C2×#13094013C2211yescharacteristic
31C2×#13094008—21no—
32C2×#13094003C2211yescharacteristic
33C2×#13094001—21no—
34C2×#13093998C2211yescharacteristic
35C2×Q8×Dic47C2211yescharacteristic
36C2×Q8×Dic47C2211yescharacteristic
37C2×#13093989—21no—
38C2×#13093989C2211yescharacteristic
39C2×#13093986C2211yescharacteristic
40C2×(C22⋊D47)⋊C4—21no—
41C2×#13093982—21no—
42C2×#13093980—21no—
43C22×C4×Dic47C2211yescharacteristic
44#15689530C2218yescomplemented
45#15689516C2218yescomplemented
46#15689490C2218yescomplemented
47#15689484C2218yescomplemented
48#15689379C2218yescomplemented
49#15689371C2218yes—
50#15689369C2218yes—
51Q16×Dic47C2218yescomplemented
52#15689215C2218yescomplemented
53#15689210C2218yescomplemented
54#15689208C2218yescomplemented
55C2×#13093958C2211yescharacteristic
56C2×#13093957C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58C2×#13093949C2211yescharacteristic
59C2×#13093948C2211yescharacteristic
60C2×#13093948C2211yescharacteristic
61C2×#13093947C2211yescharacteristic
62C2×#13093946C2211yescharacteristic
63C2×#13093944C2211yescharacteristic
64M16×Dic47C2218yescomplemented
65C2×#13093934C2211yescharacteristic
66C2×#13093934C2211yescharacteristic
67C2×C8×Dic47C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C22×Q16×C47C2211yescharacteristic
70C22×M16×C47C2211yescharacteristic
71C2×C22⋊Q8×C47C2211yescharacteristic
72C2×C22⋊Q8×C47C2211yescharacteristic
73C47×#470C2218yescomplemented
74C2×#106×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#103×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94C2311yescharacteristic
79C22×D188C2311yescharacteristic
80C22×C22⋊D47—21no—
81C23×Dic47D411yescharacteristic
82C23×Dic47D411yescharacteristic
83C22×C4×D47—21no—
84C2×#10625337—24no—
85C2×#10625337C2314yes—
86C2×#10625325—24no—
87C2×#10625325C2314yes—
88C2×#10625336—24no—
89C2×#10625336C2314yes—
90C2×#10625329—24no—
91C2×#10625329C2314yes—
92C22×C47⋊C8C2311yescharacteristic
93C22×C47⋊C8C2311yescharacteristic
94#13094023—22no—
95#13094023C2314yes—
96#13094022—22no—
97#13094022C2314yes—
98#13094019—28no—
99#13094015—22no—
100#13094015C2314yes—
101#13094014—28no—
102#13094013—22no—
103#13094013C2314yes—
104#13094008—28no—
105#13094003—22no—
106#13094003C2314yes—
107#13094001—28no—
108#13093998—22no—
109#13093998C2314yes—
110Q8×Dic47—22no—
111Q8×Dic47—22no—
112Q8×Dic47C2314yes—
113Q8×Dic47C2314yes—
114#13093989—28no—
115#13093989—22no—
116#13093989C2314yes—
117#13093986—22no—
118#13093986C2314yes—
119(C22⋊D47)⋊C4—28no—
120#13093982—28no—
121#13093980—28no—
122C2×C4⋊Dic47—21no—
123C2×C4⋊Dic47—21no—
124C2×C4⋊Dic47—21no—
125C2×C4⋊Dic47C2311yescharacteristic
126C2×C4⋊Dic47C2311yescharacteristic
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×C22⋊Dic47—21no—
134C2×(C2×D47)⋊C4—21no—
135C2×(C2×D47)⋊C4—21no—
136C2×(C2×D47)⋊C4—21no—
137C2×(C2×D47)⋊C4—21no—
138C2×C4×Dic47—21no—
139C2×C4×Dic47—21no—
140C2×C4×Dic47—21no—
141C2×C4×Dic47D411yescharacteristic
142C2×C4×Dic47D411yescharacteristic
143C2×C4×Dic47D414yes—
144C2×C4×Dic47C2311yescharacteristic
145C2×C4×Dic47C2311yescharacteristic
146C2×C4×Dic47C2314yes—
147#13093958C2314yes—
148#13093957C2314yes—
149#13093955C2314yes—
150#13093949C2314yes—
151#13093948C2314yes—
152#13093948C2314yes—
153#13093947C2314yes—
154#13093946C2314yes—
155#13093944C2314yes—
156#13093934C2314yes—
157#13093934C2314yes—
158C8×Dic47C2314yes—
159C8×Dic47C2314yes—
160C22×Q8×C47C2311yescharacteristic
161C22×Q8×C47C2311yescharacteristic
162C23×C4×C47C2311yescharacteristic
163C2×Q16×C47—24no—
164C2×Q16×C47C2314yes—
165C2×M16×C47—24no—
166C2×M16×C47C2314yes—
167C22×C8×C47C2311yescharacteristic
168C22×C8×C47C2311yescharacteristic
169C22⋊Q8×C47—22no—
170C22⋊Q8×C47—22no—
171C22⋊Q8×C47C2314yes—
172C22⋊Q8×C47C2314yes—
173C2×C4⋊C4×C47—21no—
174C2×C4⋊C4×C47—21no—
175C2×C4⋊C4×C47C2311yescharacteristic
176C2×C4⋊C4×C47C2311yescharacteristic
177C2×C22⋊C4×C47—21no—
178C2×C22⋊C4×C47—21no—
179#106×C47C2314yes—
180#103×C47C2314yes—
181#103×C47C2314yes—
182C24×C47C2×D411yescharacteristic
183C23×D47—21no—
184C2×Q8×C47—21no—
185C2×Q8×C47—21no—
186C2×Q8×C47—22no—
187C2×Q8×C47—22no—
188C2×Q8×C47—22no—
189C2×Q8×C47—22no—
190C2×Q8×C47C2412yes—
191C2×Q8×C47C2412yes—
192C22×C4×C47—22no—
193C22×C4×C47—22no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2×D412yes—
200C22×C4×C47C2412yes—
201C22×C4×C47C2411yescharacteristic
202C2×C22⋊D47—24no—
203C2×C22⋊D47—44no—
204C22×Dic47—24no—
205C22×Dic47—21no—
206C22×Dic47—21no—
207C22×Dic47—21no—
208C22×Dic47—42no—
209C22×Dic47C2×D411yescharacteristic
210C22×Dic47C2×D411yescharacteristic
211C22×Dic47C2×D411yescharacteristic
212C22×Dic47C2×D414yes—
213C22×Dic47C2×D414yes—
214C22×Dic47C2×D411yescharacteristic
215C2×D188—22no—
216C2×D188—22no—
217C2×D188—21no—
218C2×D188C2412yes—
219C2×C4×D47—24no—
220C2×C4×D47—44no—
221C2×Dic94—22no—
222C2×Dic94—22no—
223C2×Dic94—21no—
224C2×Dic94—24no—
225C2×Dic94—44no—
226C2×Dic94C2412yes—
227Q16×C47—28no—
228M16×C47—28no—
229C2×C8×C47—22no—
230C2×C8×C47#4114yes—
231C2×C8×C47C2412yes—
232C2×C8×C47C2412yes—
233C4⋊C4×C47—24no—
234C4⋊C4×C47—24no—
235C4⋊C4×C47—21no—
236C4⋊C4×C47—21no—
237C4⋊C4×C47C2412yes—
238C4⋊C4×C47C2412yes—
239C22⋊C4×C47—24no—
240C22⋊C4×C47—24no—
241C22⋊Dic47—24no—
242#10625337—28no—
243#10625336—28no—
244(C2×D47)⋊C4—24no—
245(C2×D47)⋊C4—24no—
246(C2×D47)⋊C4—24no—
247(C2×D47)⋊C4—24no—
248C4⋊Dic47—21no—
249C4⋊Dic47—21no—
250C4⋊Dic47—24no—
251C4⋊Dic47—24no—
252C4⋊Dic47—24no—
253C4⋊Dic47C2412yes—
254C4⋊Dic47C2412yes—
255Dic47⋊C4—24no—
256Dic47⋊C4—24no—
257Dic47⋊C4—24no—
258Dic47⋊C4—24no—
259Dic47⋊C4—24no—
260Dic47⋊C4—24no—
261C4×Dic47—24no—
262C4×Dic47—24no—
263C4×Dic47—24no—
264C4×Dic47C2×D414yes—
265C4×Dic47C2×D412yes—
266C4×Dic47C2×D412yes—
267C4×Dic47C2×D414yes—
268C4×Dic47C2412yes—
269C4×Dic47C2412yes—
270#10625329—28no—
271C2×C47⋊C8—22no—
272C2×C47⋊C8#4114yes—
273C2×C47⋊C8C2412yes—
274C2×C47⋊C8C2412yes—
275#10625325—28no—
276C23×C47—22no—
277C23×C47—22no—
278C23×C47—22no—
279C23×C47C22×D412yes—
280C23×C47C22×D411yescharacteristic
281C22×D47—22no—
282C22×D47—42no—
283C22×D47—42no—
284C22×D47—42no—
285Q8×C47—22no—
286Q8×C47—22no—
287Q8×C47—22no—
288Q8×C47—22no—
289Q8×C47—42no—
290Q8×C47—42no—
291C2×C4×C47—22no—
292C2×C4×C47—24no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—42no—
300C2×C4×C47—42no—
301C2×C4×C47—42no—
302C2×C4×C47—42no—
303C2×C4×C47C22×D412yes—
304C2×C4×C47C22×D411yescharacteristic
305C2×C4×C47C2×#4112yes—
306C2×C4×C47C2×#4112yes—
307C2×C4×C47C2511yescharacteristic
308C22⋊D47—48no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—28no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—44no—
317C2×Dic47—42no—
318C2×Dic47—42no—
319C2×Dic47—42no—
320C2×Dic47#13714yes—
321C2×Dic47C22×D412yes—
322C2×Dic47C22×D412yes—
323C2×Dic47C22×D412yes—
324C2×Dic47C22×D412yes—
325D188—22no—
326D188—22no—
327D188—42no—
328C4×D47—48no—
329Dic94—22no—
330Dic94—22no—
331Dic94—48no—
332Dic94—42no—
333C8×C47—22no—
334C8×C47C2×#4114yes—
335C47⋊C8—22no—
336C47⋊C8C2×#4114yes—
337C2×#3172—471nomaximal, Sylow
338C22×C47—22no—
339C22×C47—22no—
340C22×C47—22no—
341C22×C47—44no—
342C22×C47#53212yes—
343C22×C47C2×#13712yes—
344C22×C47#57512yes—
345C22×C47C23×D411yescharacteristic
346C2×D47—42no—
347C2×D47—42no—
348C2×D47—42no—
349C2×D47—84no—
350C4×C47—22no—
351C4×C47—42no—
352C4×C47—42no—
353C4×C47—42no—
354C4×C47—42no—
355C4×C47#53212yes—
356C4×C47C22×#4111yescharacteristic
357C4×C47C22×#4111yescharacteristic
358Dic47—22no—
359Dic47—22no—
360Dic47—22no—
361Dic47—42no—
362Dic47—42no—
363Dic47—42no—
364Dic47C2×#13714yes—
365C2×#533—471no—
366C2×#529—471no—
367#3172—4716no—
368C2×#501—471no—
369C2×#497—471no—
370C2×#491—471no—
371C2×#489—471no—
372C2×#470—471no—
373C2×#470D4711yescharacteristic, complemented
374C2×#468—471no—
375C2×#468—471no—
376C2×C4×Q16—471no—
377C2×C4×Q16—471no—
378C2×C4×SD16—471no—
379C2×C4×SD16—471no—
380C2×C4×M16—471no—
381C2×C47—42no—
382C2×C47#317214yescomplemented
383C2×C47C2×#53211yescharacteristic
384C2×C47C22×#13711yescharacteristic
385C2×C47C2×#57511yescharacteristic
386D47—82no—
387C22×Q16—471no—
388C22×Q16C2×D4711yescharacteristic
389C22×SD16—471no—
390C22×SD16—471no—
391C22×M16—471no—
392C22×M16C2×D4711yescharacteristic
393#533—478no—
394#533—944no—
395C2×C4⋊Q8—471no—
396C2×C4⋊Q8—471no—
397#529—478no—
398#529—944no—
399C2×#126—941no—
400C2×#125—471no—
401C2×#125—941no—
402C2×#124—471no—
403C2×#123—941no—
404C2×C22⋊Q8—471no—
405C2×C22⋊Q8—941no—
406C2×C22⋊Q8C2×D4711yescharacteristic
407C2×C22⋊Q8C2×D4711yescharacteristic
408C2×#121—471no—
409C2×C4×Q8—471no—
410C2×C4×Q8—471no—
411C2×C4×Q8—471no—
412C2×C4×Q8—941no—
413C2×C4×D4—471no—
414C2×C4×D4—941no—
415C2×#117—941no—
416C2×#117—941no—
417C22×C42—471no—
418#501—478no—
419#497—478no—
420#491—478no—
421#489—478no—
422#470—478no—
423#470C2×D4718yescomplemented
424#468—478no—
425#468—478no—
426C4×Q16—478no—
427C4×Q16—478no—
428C4×SD16—478no—
429C4×SD16—478no—
430C2×#107—471no—
431C2×#107—471no—
432C2×#106—471no—
433C2×#106C2×D4711yescharacteristic
434C2×#103—471no—
435C2×#103—471no—
436C2×#103—471no—
437C2×#103—471no—
438C2×#103C2×D4711yescharacteristic
439C2×#103C2×D4711yescharacteristic
440C2×#102—471no—
441C2×#102—471no—
442C4×M16—478no—
443C2×#97—471no—
444C2×#97—471no—
445C2×C4×C8—471no—
446C2×C4×C8—471no—
447C47C2×#317211yescharacteristic, complemented, Sylow
448C22×Q8—471no—
449C22×Q8—941no—
450C22×Q8C22×D4711yescharacteristic
451C22×Q8C22×D4711yescharacteristic
452C22×D4—471no—
453C22×D4—941no—
454C23×C4—471no—
455C23×C4—471no—
456C23×C4—941no—
457C23×C4C22×D4711yescharacteristic
458C2×Q16—24no—
459C2×Q16—474no—
460C2×Q16—944no—
461C2×Q16C22×D4714yes—
462C2×SD16—474no—
463C2×SD16—474no—
464C2×SD16—944no—
465C2×SD16—944no—
466C2×M16—24no—
467C2×M16—474no—
468C2×M16—944no—
469C2×M16C22×D4714yes—
470C22×C8—471no—
471C22×C8—471no—
472C22×C8C22×D4711yescharacteristic
473C22×C8C22×D4711yescharacteristic
474C4⋊Q8—474no—
475C4⋊Q8—474no—
476C4⋊Q8—942no—
477C4⋊Q8—942no—
478#126—948no—
479#125—474no—
480#125—942no—
481#125—948no—
482#124—474no—
483#124—942no—
484#123—948no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—474no—
488C22⋊Q8—948no—
489C22⋊Q8—942no—
490C22⋊Q8C22×D4714yes—
491C22⋊Q8C22×D4714yes—
492#121—474no—
493#121—942no—
494C4×Q8—474no—
495C4×Q8—474no—
496C4×Q8—474no—
497C4×Q8—942no—
498C4×Q8—948no—
499C4×Q8—942no—
500C4×Q8—942no—
501C4×D4—474no—
502C4×D4—942no—
503C4×D4—948no—
504#117—948no—
505#117—948no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—471no—
509C2×C4⋊C4—471no—
510C2×C4⋊C4—941no—
511C2×C4⋊C4—941no—
512C2×C4⋊C4—941no—
513C2×C4⋊C4—941no—
514C2×C4⋊C4—941no—
515C2×C4⋊C4—941no—
516C2×C4⋊C4—941no—
517C2×C4⋊C4—941no—
518C2×C4⋊C4—941no—
519C2×C4⋊C4C22×D4711yescharacteristic
520C2×C4⋊C4C22×D4711yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—941no—
524C2×C22⋊C4—941no—
525C2×C22⋊C4—941no—
526C2×C22⋊C4—941no—
527C2×C22⋊C4—941no—
528C2×C42—471no—
529C2×C42—471no—
530C2×C42—474no—
531C2×C42—471no—
532C2×C42—471no—
533C2×C42—474no—
534C2×C42—941no—
535C2×C42—941no—
536C2×C42—941no—
537#107—474no—
538#107—474no—
539#106—474no—
540#106C22×D4714yes—
541#103—474no—
542#103—474no—
543#103—474no—
544#103—474no—
545#103C22×D4714yes—
546#103C22×D4714yes—
547#102—474no—
548#102—474no—
549#97—474no—
550#97—474no—
551C4×C8—474no—
552C4×C8—474no—
553C24—941no—
554C24D4×D4711yescharacteristic
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—472no—
562C2×Q8—944no—
563C2×Q8—941no—
564C2×Q8—942no—
565C2×Q8—942no—
566C2×Q8—1884no—
567C2×Q8C23×D4712yes—
568C2×Q8C23×D4712yes—
569C2×D4—472no—
570C2×D4—944no—
571C2×D4—941no—
572C2×D4—942no—
573C2×D4—942no—
574C2×D4—1884no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—471no—
582C22×C4—474no—
583C22×C4—471no—
584C22×C4—471no—
585C22×C4—471no—
586C22×C4—474no—
587C22×C4—944no—
588C22×C4—944no—
589C22×C4—941no—
590C22×C4—941no—
591C22×C4—941no—
592C22×C4—1884no—
593C22×C4—1882no—
594C22×C4D4×D4712yes—
595C22×C4D4×D4711yescharacteristic
596C22×C4C23×D4712yes—
597C22×C4C23×D4711yescharacteristic
598Q16—28no—
599Q16—948no—
600SD16—948no—
601SD16—948no—
602M16—28no—
603M16—948no—
604C2×C8—22no—
605C2×C8—474no—
606C2×C8—472no—
607C2×C8—472no—
608C2×C8—942no—
609C2×C8#1062535214yes—
610C2×C8C23×D4712yes—
611C2×C8C23×D4712yes—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—472no—
617C4⋊C4—472no—
618C4⋊C4—944no—
619C4⋊C4—944no—
620C4⋊C4—944no—
621C4⋊C4—944no—
622C4⋊C4—944no—
623C4⋊C4—944no—
624C4⋊C4—944no—
625C4⋊C4—944no—
626C4⋊C4—944no—
627C4⋊C4—941no—
628C4⋊C4—941no—
629C4⋊C4C23×D4712yes—
630C4⋊C4C23×D4712yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—944no—
634C22⋊C4—944no—
635C22⋊C4—944no—
636C22⋊C4—944no—
637C22⋊C4—944no—
638C42—474no—
639C42—472no—
640C42—472no—
641C42—474no—
642C42—472no—
643C42—472no—
644C42—944no—
645C42—944no—
646C42—944no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—942no—
651C23—1882no—
652C23—1882no—
653C23—1882no—
654C23C2×D4×D4712yes—
655C23C2×D4×D4711yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—22no—
659Q8—22no—
660Q8—42no—
661Q8—42no—
662Q8—942no—
663Q8—942no—
664Q8—1888no—
665Q8—1882no—
666D4—942no—
667D4—942no—
668D4—1888no—
669D4—1882no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—474no—
683C2×C4—472no—
684C2×C4—472no—
685C2×C4—472no—
686C2×C4—472no—
687C2×C4—948no—
688C2×C4—942no—
689C2×C4—942no—
690C2×C4—942no—
691C2×C4—942no—
692C2×C4—942no—
693C2×C4—942no—
694C2×C4—1888no—
695C2×C4—1884no—
696C2×C4—1882no—
697C2×C4—1882no—
698C2×C4—1882no—
699C2×C4C2×D4×D4712yes—
700C2×C4C2×D4×D4711yescharacteristic
701C2×C4#41×D4712yes—
702C2×C4C2×#1062535212yes—
703C2×C4C24×D4711yescharacteristic
704C8—22no—
705C8—474no—
706C8—942no—
707C8C2×#1062535214yes—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—44no—
712C22—3764no—
713C22—1882no—
714C22—1882no—
715C22—1882no—
716C22#1568966812yes—
717C22#137×D4712yes—
718C22#1568992212yes—
719C22C22×D4×D4711yescharacteristic
720C4—22no—
721C4—42no—
722C4—42no—
723C4—42no—
724C4—42no—
725C4—474no—
726C4—942no—
727C4—942no—
728C4—942no—
729C4—1882no—
730C4—1882no—
731C4—1882no—
732C4#1568966812yes—
733C4C2×#41×D4711yescharacteristic
734C4C22×#1062535211yescharacteristic
735C2—42no—
736C2—3762no—
737C2#2025398914yesdirect product factor
738C2C2×#1568966811yescharacteristic
739C2C2×#137×D4711yescharacteristic
740C2C2×#1568992211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#470C2
socleC23×C47C22×D4
prime radicalC2×#13093998C22
hypercenterC2×#470D47
hypocenterC47C2×#3172
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#15689675C2semidirect
3. #20253989C2direct (N × H)
4. C2×#15689530C2semidirect
5. C2×#15689516C2semidirect
6. C2×#15689490C2semidirect
7. C2×#15689484C2semidirect
8. C2×#15689379C2semidirect
11. C2×Q16×Dic47C2semidirect
12. C2×#15689215C2semidirect
13. C2×#15689210C2semidirect
14. C2×#15689208C2semidirect
15. C2×M16×Dic47C2semidirect
16. C2×C47×#470C2semidirect
22. #15689675C22semidirect
44. #15689530C22semidirect
45. #15689516C22semidirect
46. #15689490C22semidirect
47. #15689484C22semidirect
48. #15689379C22semidirect
51. Q16×Dic47C22semidirect
52. #15689215C22semidirect
53. #15689210C22semidirect
54. #15689208C22semidirect
64. M16×Dic47C22semidirect
73. C47×#470C22semidirect
373. C2×#470D47semidirect
382. C2×C47#3172semidirect
423. #470C2×D47semidirect
447. C47C2×#3172semidirect
737. C2#20253989direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#156896752
C2×#156896592
#202539892
C2×#156895302
C2×#156895162
C2×#156894902
C2×#156894842
C2×#156893792
C2×#156893712
C2×#156893692
C2×Q16×Dic472
C2×#156892152
C2×#156892102
C2×#156892082
C2×M16×Dic472
C2×C47×#4702
C2×#317247